9.8 Determining cosmic parameters 389showed that to keep the first peak heightH 1 fixed, the baryon density can be
increased only simultaneously with the dark matter density. That is, baryonic and
dark matter work in opposite directions in terms of their effect on the first peak.
Now we have seen that the second peak decreases as the baryon density increases.
For the second peak, it turns out that an increase in cold dark matter density has a
similar effect. Hence, the baryon density and the dark matter density work in the
same direction in terms of how they alter the height of the second peak. This is
because the positive contributionO 2 ∝To^2 decreases more rapidly than the negative
contributionO 1 ∝ToTpas (^) mh^275 increases. Using both peak heights enables us
to determine both the baryon density and the cold dark matter density and thus
to resolve the degeneracy in the determination of (^) mh^275 and (^) bh^275. For instance,
assuming that the universe is flat and that cold matter constitutes 100% of the critical
density, we can fit the data for the height of the first peak only if (^) b 0 .08 for
H=70 km s−^1 Mpc−^1 .However, in this case the second acoustic peak is absent.
It reappears only when we simultaneously decrease the cold dark matter and the
baryon density. Therefore, based on the data, the combination of the first acoustic
peak height with the fact that the second peakexistsinforms us that the cold dark
matter density cannot exceed half of the critical density and that the baryon density
is less than 8% of the critical density. Although these limit can be improved greatly
by an analysis of the full anisotropy power spectrum and other observations, it is
important to appreciate thatthe height of the first peak together with the existence
of the second peak are in themselves convincing evidence of the following key
qualitative features of our universe: that the total cold matter density is less than
the critical density, that cold dark matter exists and that its density exceeds the
baryon density.
Combining peak height and locationIf information about the first two peak heights
determines the baryon and matter density (of course, in combination withh 75 ), then
adding information about the first peak location fixes the spatial curvature precisely.
Data strongly suggest that the universe is flat and that the total energy density is
equal to the critical density. At the same time, the peak heights suggest that the dark
matter and baryon densities are significantly less than the critical density. Hence,
some form of dark energy must make up the difference and dominate the density
of the universe today.
Hence, combining peak heights and their location we can conclude that dark
energy exists.Note that this line of argument is totally independent of the su-
pernova luminosity–redshift test (see Section 2.5.2), which leads to the same
conclusion.
Since the heights of the peaks depend on (^) mh^275 and their locations on (^) mh^375.^1 ,
we can squeeze out even more information; namely, we can determine the Hubble